How to animate petals opening
so, with Dupliverts:


Create your circle, create your petal, apply the rotations, parent the petal to a bone With Automatic Weight.
Select your circle, in the Properties panel > Object > Duplication, press the Verts button, enable Rotation.
Parent the armature to the circle. The petal should duplicate along the circle.
Animate the bone in Pose mode, it animates the other petals.